Average Error: 0.4 → 0.1
Time: 4.2s
Precision: 64
\[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]
↓
\[\mathsf{fma}\left(120, a, \frac{60}{z - t} \cdot \left(x - y\right)\right)\]
\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120
↓
\mathsf{fma}\left(120, a, \frac{60}{z - t} \cdot \left(x - y\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r850831 = 60.0;
        double r850832 = x;
        double r850833 = y;
        double r850834 = r850832 - r850833;
        double r850835 = r850831 * r850834;
        double r850836 = z;
        double r850837 = t;
        double r850838 = r850836 - r850837;
        double r850839 = r850835 / r850838;
        double r850840 = a;
        double r850841 = 120.0;
        double r850842 = r850840 * r850841;
        double r850843 = r850839 + r850842;
        return r850843;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r850844 = 120.0;
        double r850845 = a;
        double r850846 = 60.0;
        double r850847 = z;
        double r850848 = t;
        double r850849 = r850847 - r850848;
        double r850850 = r850846 / r850849;
        double r850851 = x;
        double r850852 = y;
        double r850853 = r850851 - r850852;
        double r850854 = r850850 * r850853;
        double r850855 = fma(r850844, r850845, r850854);
        return r850855;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.4
Target0.2
Herbie0.1
\[\frac{60}{\frac{z - t}{x - y}} + a \cdot 120\]

Derivation

  1. Initial program 0.4

    \[\frac{60 \cdot \left(x - y\right)}{z - t} + a \cdot 120\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\mathsf{fma}\left(120, a, \frac{60 \cdot \left(x - y\right)}{z - t}\right)}\]
  3. Using strategy rm

  4. Applied associate-/l*0.1

    \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{\frac{60}{\frac{z - t}{x - y}}}\right)\]
  5. Using strategy rm

  6. Applied associate-/r/0.1

    \[\leadsto \mathsf{fma}\left(120, a, \color{blue}{\frac{60}{z - t} \cdot \left(x - y\right)}\right)\]

  7. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(120, a, \frac{60}{z - t} \cdot \left(x - y\right)\right)\]

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x y z t a)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (+ (/ 60 (/ (- z t) (- x y))) (* a 120))

  (+ (/ (* 60 (- x y)) (- z t)) (* a 120)))